CUET Mathematics 2025 13 May Shift 2 PYQs

If A and B are independent events such that $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$, then the value of $P(A \cap B)$ is equal to

If the binomial distribution $X\sim B(n, p)$ of mean 3 and variance $\frac{3}{2}$ $(p + q) = 1$, then which of the following is/are TRUE?

(A) $q = \frac{1}{2}$, $n = 6$

(B) $P(X \leq 5) = \frac{63}{64}$, $p = \frac{1}{2}$

(C) $q = \frac{1}{3}$, $p = \frac{2}{3}$

(D) $P(X = 4) = \frac{15}{64}$, $n = 6$

Choose the correct answer from the options given below:

A bag contains 4 red and 6 green balls. A ball is drawn at random. Its colour is noted and is returned to the bag. One additional ball of the colour drawn is put in the bag. Again a ball is then drawn from the bag. The probability of this ball to be of green colour is